Problem: Divide. Write your answer in simplest form. $ \dfrac{1}{7} \div \dfrac{5}{2} = {?} $
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{5}{2}$ is $\dfrac{2}{5}$. Therefore: $ \dfrac{1}{7} \div \dfrac{5}{2} = \dfrac{1}{7} \times \dfrac{2}{5} $ $ \phantom{\dfrac{1}{7} \div \dfrac{5}{2}} = \dfrac{1 \times 2}{7 \times 5} $ $ \phantom{\dfrac{1}{7} \div \dfrac{5}{2}} = \dfrac{2}{35} $